Overcast sky luminance and illuminance Lvoc, Evoc--Algorithm 1.33

The standard CIE overcast sky is defined only as a relative luminance distribution.

a. Luminance distribution

Input
Altitude of sky point, g radians

Equation
The luminance at altitude g, Lvoc(g), is, as a fraction of the zenith luminance, Lvocz ,

Source
CIE(1)

b. Relative illuminance

Input
Tilt of surface from the horizontal (or zenith angle of surface normal), q radians

Equation

Note
If the sky luminance is given in cd/m2, the units of illuminance are lux.
Illuminance from ground-reflected light is given in algorithm 1.41

Source
Wilkinson(2)

c. Absolute illuminance

The actual illuminance under an overcast sky can vary greatly. The following empirical equation gives an indication of the average horizontal illuminance, but it should be noted that there is a very large scatter of measured values at every solar altitude.

Input
Solar altitude, gs radians

Equation

Source
Krochmann(3)

References
  1. Commission Internationale de lĠEclairage 3.2 Natural daylight: official recommendations 13th Session (1955 ) Commission Internationale de lĠEclairage, Paris
  2. Wilkinson M A Natural lighting under translucent domes Lighting Research and Technology 24 (3) 117-126 (1992)
  3. Krochmann J and Seidl M Quantitative data on daylight for illuminating engineering Lighting Research and Technology 6 (3) 165-171 (1974)

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